Cosmogenic ultra-high energy neutrinos are important to reveal new features of the Universe. After around ten years of
measurements, the IceCube Collaboration has observed plenty of neutrino events with energies above 30 TeV, including a few PeV scale events [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. However, the source of these ultra-high energy cosmic neutrinos still remains obscure. The neutrino emission associated with gamma-ray burst (GRB) was proposed from the fireball model of GRBs [7]}, [8]}, [9]}, [10]}. By associating GRBs and some lower energy neutrinos with time difference of several hundred seconds, the IceCube Collaboration [11]}, [12]}, [13]} proposed constraints on GRB neutrinos with a small flux to exclude some fireball models [9]}, [15]}.
